253389edo: Difference between revisions
Tristanbay (talk | contribs) Giving most edo pages over 100000 the mathematical interest note |
Royalmilktea (talk | contribs) m more harmonics |
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|253389}} | {{Harmonics in equal|253389|columns=11}} | ||
{{Harmonics in equal|253389|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 253389edo (continued)}} | |||
Latest revision as of 22:11, 23 September 2026
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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown. |
| ← 253388edo | 253389edo | 253390edo → |
253389 equal divisions of the octave (abbreviated 253389edo or 253389ed2), also called 253389-tone equal temperament (253389tet) or 253389 equal temperament (253389et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 253389 equal parts of about 0.00474 ¢ each. Each step represents a frequency ratio of 21/253389, or the 253389th root of 2.
253389edo is distinctly consistent to the 59-odd-limit, and indeed is the first edo to achieve it. For that reason, it might attract considerable attention from those who are not put off by extremely small step sizes.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | -0.00030 | -0.00018 | +0.00068 | +0.00039 | +0.00133 | -0.00058 | -0.00050 | +0.00076 | +0.00025 | +0.00072 |
| Relative (%) | +0.0 | -6.3 | -3.8 | +14.4 | +8.2 | +28.0 | -12.2 | -10.5 | +16.0 | +5.4 | +15.1 | |
| Steps (reduced) |
253389 (0) |
401612 (148223) |
588351 (81573) |
711353 (204575) |
876582 (116415) |
937651 (177484) |
1035718 (22162) |
1076378 (62822) |
1146221 (132665) |
1230959 (217403) |
1255339 (241783) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.00085 | +0.00121 | +0.00095 | +0.00135 | -0.00017 | -0.00019 | +0.00188 | -0.00130 | -0.00129 | -0.00216 | +0.00142 |
| Relative (%) | -17.9 | +25.5 | +20.0 | +28.5 | -3.6 | -4.0 | +39.7 | -27.4 | -27.3 | -45.5 | +30.0 | |
| Steps (reduced) |
1320018 (53073) |
1357545 (90600) |
1374956 (108011) |
1407472 (140527) |
1451392 (184447) |
1490597 (223652) |
1502784 (235839) |
1537080 (16746) |
1558278 (37944) |
1568433 (48099) |
1597309 (76975) | |